A114324 Number of partitions of n with a product greater than n.

1, 0, 0, 0, 0, 1, 3, 6, 10, 16, 26, 39, 56, 79, 111, 150, 200, 265, 349, 453, 586, 749, 957, 1209, 1522, 1903, 2379, 2950, 3654, 4500, 5534, 6771, 8271, 10063, 12228, 14799, 17884, 21543, 25919, 31087, 37233, 44477, 53063, 63149, 75059, 89014, 105436, 124631

Offset: 0

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn

Comments

The Heinz numbers of these partitions are given by A325037. - Gus Wiseman, Mar 27 2019

Examples

			a(6) = 3 since there are 3 partitions of 6 with product greater than 6: {3,3}, {2,2,2}, {4,2}.
From _Gus Wiseman_, Mar 27 2019: (Start)
The a(5) = 1 through a(9) = 16 partitions:
  (32)  (33)   (43)    (44)    (54)
        (42)   (52)    (53)    (63)
        (222)  (322)   (62)    (72)
               (331)   (332)   (333)
               (421)   (422)   (432)
               (2221)  (431)   (441)
                       (521)   (522)
                       (2222)  (531)
                       (3221)  (621)
                       (3311)  (3222)
                               (3321)
                               (4221)
                               (4311)
                               (5211)
                               (22221)
                               (32211)
(End)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Pankaj Jyoti Mahanta, On the number of partitions of n whose product of the summands is at most n, arXiv:2010.07353 [math.CO], 2020.

Crossrefs

Cf. A001055, A028422, A096276, A114324, A301987, A319000, A319005, A319916, A325037, A325038, A325044.

Programs

Mathematica

<< DiscreteMath`Combinatorica`; lst=Table[Length@Select[Partitions[n], (Times @@ # > n) &],{n,50}]
Table[Length[Select[IntegerPartitions[n],Times@@#>n&]],{n,0,20}] (* Gus Wiseman, Mar 27 2019 *)

Extensions

a(0) = 1 prepended by Gus Wiseman, Mar 27 2019